Pythagoras Theorem Worksheet — KS3 — Intermediate
Pythagoras Theorem worksheet for Key Stage 3 / Year 7-9 (Ages 11-14). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.
Exploring Pythagoras' Theorem
Key Stage 3 / Year 7-9 (Ages 11-14) - Intermediate
Instructions: This worksheet will help you understand and apply Pythagoras' Theorem. You'll solve problems involving right-angled triangles, calculate missing side lengths, and explore real-world applications. Ensure you show all your workings clearly.
Understanding Pythagoras' Theorem
Review the statement of Pythagoras' Theorem. Then, solve the problems below by identifying the hypotenuse and calculating its length. Show all your workings.
1. In a right-angled triangle, the two shorter sides are 3 cm and 4 cm. Find the length of the hypotenuse. [3 marks]
2. A triangle has sides of 5 cm and 12 cm. Determine the hypotenuse. [3 marks]
Finding Missing Sides
Use Pythagoras' Theorem to find the missing side of each right-angled triangle. Remember to square the lengths of the sides and solve for the unknown.
1. The hypotenuse is 13 cm, and one side is 5 cm. Find the other side. [3 marks]
2. One side is 8 cm, and the hypotenuse is 10 cm. Calculate the other side. [3 marks]
Real-World Applications
Apply Pythagoras' Theorem to solve real-world problems. Read each scenario carefully and calculate the required length.
1. A ladder is leaning against a wall. The base of the ladder is 6 m from the wall, and the ladder reaches a height of 8 m on the wall. Find the length of the ladder. [4 marks]
2. A rectangular park measures 40 m by 30 m. Calculate the diagonal distance across the park. [4 marks]
Problem Solving with Pythagoras
Solve these problems using Pythagoras' Theorem. Ensure you write down each step of your calculations.
1. A triangle has sides of 9 cm and 12 cm. Find the hypotenuse. [3 marks]
2. The hypotenuse of a triangle is 15 cm, and one side is 9 cm. What is the length of the other side? [3 marks]
Exploring Triangles
Determine whether the following sets of numbers can form the sides of a right-angled triangle using Pythagoras' Theorem.
1. 7 cm, 24 cm, 25 cm [3 marks]
2. 10 cm, 24 cm, 26 cm [3 marks]
Calculating Perimeters
Calculate the perimeter of each triangle using Pythagoras' Theorem to find any missing sides. Add all the sides to find the perimeter.
1. A triangle with sides 6 cm and 8 cm. Find the perimeter. [4 marks]
2. A triangle with a hypotenuse of 17 cm and one side of 8 cm. Calculate the perimeter. [4 marks]
Advanced Pythagorean Problems
Challenge yourself with these advanced problems. Use Pythagoras' Theorem to find the unknown sides.
1. A triangle has sides 15 cm and 20 cm. Determine the hypotenuse. [4 marks]
2. The hypotenuse is 25 cm, and one side is 7 cm. Find the other side. [4 marks]
Investigating Pythagorean Triples
Identify whether the following sets of numbers are Pythagorean triples. Use the theorem to verify your answers.
1. 8 cm, 15 cm, 17 cm [3 marks]
2. 9 cm, 12 cm, 15 cm [3 marks]
Activity 1: 5 cm ; 13 cm
Activity 2: 12 cm ; 6 cm
Activity 3: 10 m ; 50 m
Activity 4: 15 cm ; 12 cm
Activity 5: Yes ; Yes
Activity 6: 24 cm ; 42 cm
Activity 7: 25 cm ; 24 cm
Activity 8: Yes ; Yes
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